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A249247
Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.
4
1, 1, 1, 2, 3, 6, 10, 1, 24, 42, 7, 120, 216, 45, 1, 720, 1320, 312, 13, 5040, 9360, 2400, 136, 1, 40320, 75600, 20520, 1400, 21, 362880, 685440, 194040, 15000, 325, 1, 3628800, 6894720, 2016000, 170520, 4650, 31, 39916800, 76204800, 22861440, 2069760, 66150
OFFSET
1,4
COMMENTS
The polynomial p(n,x) is the numerator of the rational function given by f(n,x) = n - 1 + x/f(n-1,x), where f(n,1) = 1.
LINKS
EXAMPLE
f(1,x) = 1/1, so that p(1,x) = 1
f(2,x) = (1 + x)/1, so that p(2,x) = 1 + x;
f(3,x) = (2 + 3 x)/(1 + x), so that p(3,x) = 2 + 3 x.
First 7 rows of the triangle of coefficients:
1
1 1
2 3
6 10 1
24 42 7
120 216 45 1
720 1320 312 13
MATHEMATICA
z = 14; f[n_, x_] := n - 1 + x/f[n - 1, x]; f[1, x_] = 1;
t = Table[Factor[f[n, x]], {n, 1, z}]
u = Numerator[t]
TableForm[Table[CoefficientList[u[[n]], x], {n, 1, z}]] (* A249247 array *)
v = Flatten[CoefficientList[u, x]] (* A249247 sequence *)
CROSSREFS
Cf. A249248.
Sequence in context: A077753 A353122 A058911 * A276956 A276946 A191542
KEYWORD
nonn,tabf,easy
AUTHOR
Clark Kimberling, Oct 24 2014
STATUS
approved